Perturbed Riemann problem for a scalar Chapman-Jouguet combustion model

The author considers the perturbed Riemann problem for a scalar Chapman-Jouguet combustion model which comes from Majda’s model with a modified, bump-type ignition function proposed in the results of Lyng and Zumbrun in 2004. Under the entropy conditions, the unique solution in a neighborhood of the origin on the (x, t) plane (t > 0) is obtained. It is found that, for some cases, the perturbed Riemann solutions are essentially different from the corresponding Riemann solutions. The perturbation may transform a strong detonation into a weak deflagration in the neighborhood of the origin. Especially, it can be observed that burning happens although the corresponding Riemann solution does not contain combustion wave, which exhibits the instability for the unburnt state.